Playtime issue with animations
This sounds like the child objects have impact on the physics.
I assume your helicopter is rigid-body. That means it can collide with other objects such as static objects.
Now you parent the character object to the helicopter. I guess the character object is still static (or was dynamic and becomes static via parenting).
The problem is that the character object collides with the helicopter. The helicopter (as rigid body) will change position due to the impact. As the character object is parented to the helicopter the collision will always be present, making the helicopter move even further.
Solution
Ensure there is no collision between parent and child.
This can be by making the child ghost or by ensuring there is no intersecting face between the different physics meshes.